REALITY

Compositional reality is of three types: Direct, as when a table is conceived (and indeed seen) to be composed of parts (legs, top), and, finally, of the material (wood, steel, or whatever it may be) from which it is made;

Indirect, as when its chemical and physical composition, its final atomic composition, is meant;

Mathematic, as when (this being the case of a being in space) its geometric aspect or form is considered.

Now compositional reality is true reality in so far as its data are of the same type as that of Simple reality. The only true reality of the compositional type is the one I have called direct; for the legs and top of the table, as also the material from which the table is made, are visible in the same manner as the whole table is visible. Nevertheless there is here a process of analysis; simple but real.

Mathematic reality is no longer reality at all. The form, weight and size of the table are of this type. These are all given, indeed, by senses; but by a particular use of the senses. (...)

Indirect reality is still furthet from the primary sense-impression.

A table has weight, has form, has size. These things are properties of the table, but they do not compose the table to the senses. Similarly a table has a final atomic structure, that of the material or materials from which it is made.

Now these «realities» that make up the table are of the same kind. The atom — the final element, physical element, whatever it may be — «exists» in exactly the same manner as the weight, or the size, or the shape of the table exists.

Neither each, nor all, of these things taken together in any conceivable way constitute the table. It is the table that is constituted, to us, by them.

These things are all DIMENSIONS. Weight, size, atomic constitution, are as much dimensions of the table as its height, width and depth are. These 3 last are decompositions of the geometric constitution of the table. The atoms are similarly decompositions of the (...)

There need be no inquiry into the infinite, or not infinite, divisibility of the physical ultimate. The physical ultimate is no more and no less than the mathematical ultimate, which is the point. To inquire into the infinite, or not infinite, divisibility of the physical ultimate, is to TRANSFER TO THE PHYSICAL, ULTIMATE CHARACTERISTICS WHICH BELONG TO THE MATHEMATICAL ULTIMATE.

Atoms, the physical ultimates, do not exist in space; they exist in things which exist in space. Yet these things do not exist in space in virtue of physical, but of mathematical, composition.

It is as if we were to speak of the weight of a straight line, thus transferring one characteristic...

Now, whereas a table is a reality, for it is a datum of the senses, the composition of the table is not a reality in the same sense, because it is a datum, not of the senses, but of the analysis, however rudimentary and spontaneous, of sense-impressions.

But an analysis of sense-impression is an analysis, not of reality — for reality, being only reality in so far as it is perceived and only really and fully perceived in so far as it is only perceived and not analysed or reasoned about — but of an impression of reality. Compositional reality cannot therefore be understood unless it is studied in the percipient and not in the perceived.

A dimension is therefore only comprehensible in so far as the percipient is studied. Now a dimension being of space («dimension» in the usual geometrical meaning), to understand a dimension we must conceive the percipient as an experiencer of space, or in space; and this means that we must consider him as having a position.

This simplifies matters at once. We have proved (?) that a real body is composed of an infinite number of dimensions. Why then do we speak normally of only three dimensions?

Why is it impossible to us to conceive — except transferentially, non-sensively, by mathematical conception — of four or more dimensions? Because sight, which gives that sense of space on which dimensions are conceived, is static, from one point at a time. If we could travel round a sphere in a right line, tracing a circle round it, or, in other words, following a circle of its geometric composition, and if we could [do] this either in no time, extra-temporally, or receive the sense impression of the whole only at the end and then instantaneously and totally, we would have the notion of a straight line, or of a point, and not of a circumference. There is, then, nothing mysterious in this conflict between the inevitable three dimensions of sense-conception (so to speak) and the possible more of mathematical analysis (?). Position limits our concept of dimensions.

If, again, we could see an object from two sides at the same time (which, be it noted, is not the same thing as being two persons in different points of space, but the same person with the same eyes in two places) an immediate new concept of dimensions would appear to us.

It must be strictly understood that when we say that a solid is composed of an infinite number of dimensions, we mean that infinite number of dimensions to signify geometrical dimensions. We do not mean extra-geometrical properties — such as weight, size, colour — to be taken as «dimensions».

The dimensions are exclusively spatial, the body has an infinite number of dimensions strictly and exclusively from the spatial standpoint, as a thing existing in space and not «in weight», «in colour», «in size»

It may be said that the notion of inifinite divisibility is numerical and not geometric — that there is no reason to exclude this from the physical ultimate, unless it be excluded, also, from the geometric ultimate.

Infinite divisibility, however, means something else. Divisibility of the kind meant implies space.

Divisibility in general does not; it implies only number. When we say that six divided by three is two, we do not refer to any spatial operation.

The concept of plurality is all that is needed for this.